$A$ $B$ $C$ If: $ BC = 5x + 2$, $ AB = 9x + 9$, and $ AC = 95$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {9x + 9} + {5x + 2} = {95}$ Combine like terms: $ 14x + 11 = {95}$ Subtract $11$ from both sides: $ 14x = 84$ Divide both sides by $14$ to find $x$ $ x = 6$ Substitute $6$ for $x$ in the expression that was given for $BC$ $ BC = 5({6}) + 2$ Simplify: $ {BC = 30 + 2}$ Simplify to find ${BC}$ : $ {BC = 32}$